# NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Written by Team Trustudies
Updated at 2021-02-11

## NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.6

Q.1 Solve
(a)$\frac{2}{3}+\frac{1}{7}$
(b)$\frac{3}{10}+\frac{7}{15}$
(c) $\frac{4}{9}+\frac{2}{7}$
(d) $\frac{5}{7}+\frac{1}{3}$
(e) $\frac{2}{5}+\frac{1}{6}$
(f) $\frac{4}{5}+\frac{2}{3}$
(g) $\frac{3}{4}?\frac{1}{3}$
(h) $\frac{5}{6}?\frac{1}{3}$
(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
(k) $1\frac{1}{3}+3\frac{2}{3}$
(l) $4\frac{2}{3}+3\frac{1}{4}$
(m) $\frac{16}{5}?\frac{7}{5}$
(n) $\frac{4}{3}?\frac{1}{2}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a)$\frac{2}{3}+\frac{1}{7}$
LCM of 7 and 3 = 21
$\frac{2×7}{3×7}+\frac{1×3}{7×3}$
= $\frac{14}{21}+\frac{3}{21}$
= $\frac{17}{21}$
(b)$\frac{3}{10}+\frac{7}{15}$
LCM of 10 and 15 = 30
$\frac{3×3}{10×3}+\frac{7×2}{15×2}$
= $\frac{9}{30}+\frac{14}{30}$
= $\frac{23}{30}$
(c) $\frac{4}{9}+\frac{2}{7}$
LCM of 9 and 7 = 63
$\frac{4×7}{9×7}+\frac{2×9}{7×9}$
= $\frac{28}{63}+\frac{18}{63}$
= $\frac{46}{63}$
(d) $\frac{5}{7}+\frac{1}{3}$
LCM of 7 and 3 = 21
$\frac{5×3}{7×3}+\frac{1×7}{3×7}$
= $\frac{15}{21}+\frac{7}{21}$
= $\frac{22}{21}$
(e) $\frac{2}{5}+\frac{1}{6}$
LCM of 5 and 6 = 30
$\frac{2×6}{5×6}+\frac{1×5}{6×5}$
= $\frac{12}{30}+\frac{5}{30}$
= $\frac{17}{30}$
(f) $\frac{4}{5}+\frac{2}{3}$
LCM of 5 and 3 = 15
$\frac{4×3}{5×3}+\frac{2×5}{3×5}$
= $\frac{12}{15}+\frac{10}{15}$
= $\frac{22}{15}$
(g) $\frac{3}{4}?\frac{1}{3}$
LCM of 4 and 3 = 12
$\frac{3×3}{4×3}?\frac{1×4}{3×4}$
= $\frac{9}{12}?\frac{4}{12}$
= $\frac{5}{12}$
(h) $\frac{5}{6}?\frac{1}{3}$
LCM of 6 and 3 = 6
$\frac{5}{6}?\frac{1×2}{3×2}$
= $\frac{5}{6}?\frac{2}{6}$
= $\frac{3}{6}$ = $\frac{1}{2}$
(i) $\frac{2}{3}+\frac{3}{4}+\frac{1}{2}$
LCM of 3, 4 and 2 = 12
$\frac{2×4}{3×4}+\frac{3×3}{4×3}+\frac{1×6}{2×6}$
$\frac{8}{12}+\frac{9}{12}+\frac{6}{12}$
$\frac{23}{12}$
(j) $\frac{1}{2}+\frac{1}{3}+\frac{1}{6}$
LCM of 2, 3 and 6 = 6
$\frac{1×3}{2×3}+\frac{1×2}{3×2}+\frac{1}{6}$
$\frac{3}{6}+\frac{2}{6}+\frac{1}{6}$
$\frac{6}{6}$ = 1
(k) $1\frac{1}{3}+3\frac{2}{3}$
= $\frac{4}{3}+\frac{11}{3}$
= $\frac{15}{3}$ = 5
(l) $4\frac{2}{3}+3\frac{1}{4}$
= $\frac{14}{3}+\frac{13}{4}$
LCM of 3 and 4 = 12
$\frac{14×4}{3×4}+\frac{13×3}{4×3}$
= $\frac{56}{12}+\frac{39}{12}$
= $\frac{95}{12}$ \)
(m) $\frac{16}{5}?\frac{7}{5}$
$\frac{9}{5}$ = $1\frac{4}{5}$
(n) $\frac{4}{3}?\frac{1}{2}$
LCM of 3 and 2 = 6
$\frac{4×2}{3×2}?\frac{1×3}{2×3}$
= $\frac{8}{6}?\frac{3}{6}$
= $\frac{5}{6}$ \)

Q.2 Sarita bought $\frac{2}{5}$ metre of ribbon and Lalita $\frac{3}{4}$ metre of ribbon. What is the total length of the ribbon they bought?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Length of ribbon bought by Sarita = $\frac{2}{5}$ metre
Length of ribbon bought by Lalita = $\frac{3}{4}$ metre
$?$ Length of ribbon bought by Sarita and Lalita $\frac{2}{5}+\frac{3}{4}$
LCM of 5 and 4 = 20
$\frac{2×4}{5×4}+\frac{3×5}{4×5}$
= $\frac{8}{20}+\frac{15}{20}$
= $\frac{23}{20}$ = $1\frac{3}{20}$ meter

Q.3 Naina was given $1\frac{1}{2}$ piece of cake and Najma was given $1\frac{1}{3}$ piece of cake. Find the total amount of cake was given to both of them.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Fraction of cake Naina got = $1\frac{1}{2}$ = $\frac{3}{2}$
Fraction of cake Najma got = $1\frac{1}{3}$= $\frac{4}{3}$
Total amount of cake given to both of them =
$\frac{3}{2}+\frac{4}{3}$
LCM of 2 and 3 = 6
$\frac{3×3}{2×3}+\frac{4×2}{3×2}$
= $\frac{9}{6}+\frac{8}{6}$
= $\frac{17}{6}$ = $2\frac{5}{6}$

Q. 4. Fill in the boxes:
(a) $??\frac{5}{8}=\frac{1}{4}$
(b) $??\frac{1}{5}=\frac{1}{2}$
(c) $\frac{1}{2}??=\frac{1}{6}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) $??\frac{5}{8}=\frac{1}{4}$
Or, $?=\frac{1}{4}+\frac{5}{8}$
= $\frac{1×2}{4×2}+\frac{5}{8}$
= $\frac{2}{8}+\frac{5}{8}$ = $\frac{7}{8}\left(b\right){\text{\(}}??\frac{1}{5}=\frac{1}{2}$
Or, $?=\frac{1}{2}+\frac{1}{5}$
= $\frac{1×5}{2×5}+\frac{1×2}{5×2}$
= $\frac{5}{10}+\frac{2}{10}$ = $\frac{7}{10}$
(C) $\frac{1}{2}??=\frac{1}{6}$
Or, $\frac{1}{2}?\frac{1}{6}=?$
Or, $?=\frac{1×3}{2×3}?\frac{1}{6}$
Or, $?=\frac{3}{6}?\frac{1}{6}$
Or, $?=\frac{2}{6}$ = $\frac{1}{3}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Q6 A piece of wire $\frac{7}{8}$ metre long broke into two pieces. One piece was $\frac{1}{4}$ metre long. How long is the other piece?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Total length of wire = $\frac{7}{8}$ metre
Length of one piece of wire = $\frac{1}{4}$metre
Length of other piece of wire = Length of the original wire and this one piece of wire
= $\frac{7}{8}?\frac{1}{4}$
= $\frac{7}{8}?\frac{1×2}{4×2}$
= $\frac{7}{8}?\frac{2}{8}$
= $\frac{5}{8}$

Q.7 Nandini’s house is $\frac{9}{10}$ km from her school. She walked some distance and then took a bus for $\frac{1}{2}$ km to reach the school. How far did she walk?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Distance of the school from house = $\frac{9}{10}$ km
Distance she travelled by bus = $\frac{1}{2}$ km
Distance walked by Nandini = Total distance of the school – Distance she travelled by bus
= $\frac{9}{10}?\frac{1}{2}$
= $\frac{9}{10}?\frac{1×5}{2×5}$
= $\frac{9}{10}?\frac{5}{10}$
= $\frac{4}{10}$ = $\frac{2}{5}$ km

Q.8 Asha and Samuel have bookshelves of the same size partly filled with books. Asha’s shelf is $\frac{5}{6}$ th full and Samuel’s shelf is $\frac{2}{5}$ th full. Whose bookshelf is more full? By what fraction?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Fraction of Asha’s bookshelf = $\frac{5}{6}$
Fraction of Samuel’s bookshelf = $\frac{2}{5}$
$\frac{5}{6}$ and $\frac{2}{5}$
By cross multiplication
5×5 and 6×2
25 > 12
$\frac{5}{6}$ > $\frac{2}{5}$
$?$ Asha’s bookshelf is more full than Samuel’s bookshelf
Difference = $\frac{5}{6}$ - $\frac{2}{5}$
= $\frac{5×5}{6×5}$ - $\frac{2×6}{5×6}$
= $\frac{25}{30}$ - $\frac{12}{30}$
= $\frac{13}{30}$

Q.9 Jaidev takes$2\frac{1}{5}$ minutes to walk across the school ground. Rahul takes$\frac{7}{4}$ minutes to do the same. Who takes less time and by what fraction?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Time taken by Jaidev to walk across the school ground =$2\frac{1}{5}$ = $\frac{11}{5}$ minutes
Time taken by Rahul to walk across the school ground = $\frac{7}{4}$ minutes
$\frac{11}{5}$ and $\frac{7}{4}$
By cross multiplication
11×4 and 5×7
44 > 35
$\frac{11}{5}$ > $\frac{7}{4}$
$?$ Rahul takes less time than Jaidev to walk across the school ground
Difference = $\frac{11}{5}$ - $\frac{7}{4}$
= $\frac{11×4}{5×4}$ - $\frac{7×5}{4×5}$
= $\frac{44}{20}$ - $\frac{35}{20}$
= $\frac{9}{20}$

## NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.1

Q.1 Write the fraction representing the shaded portion.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(i) Number of parts = 4
$?$ Fraction = $\frac{2}{4}$
(ii) Number of parts = 9
$?$ Fraction = $\frac{8}{9}$
(iii) Number of parts = 8
$?$ Fraction = $\frac{4}{8}$
(iv) Number of parts = 4
$?$ Fraction = $\frac{1}{4}$
(v) Number of parts = 7
$?$ Fraction = $\frac{3}{7}$
(vi) Number of parts = 12
$?$ Fraction = $\frac{3}{12}$
(vii) Number of parts = 10
$?$ Fraction = $\frac{10}{10}$
(viii) Number of parts = 9
$?$ Fraction = $\frac{4}{9}$
(ix) Number of parts = 8
$?$ Fraction = $\frac{4}{8}$
(x) Number of parts = 2
$?$ Fraction = $\frac{1}{2}$

Q.2 Colour the part according to the given fraction.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Q.3 Identify the error, if any.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(i) The parts are not equal
Hence, this is not $\frac{1}{2}$
(ii) the parts are not equal
Hence, Shaded portion is not $\frac{1}{4}$
(iii) the parts are not equal
Hence, Shaded portion is not $\frac{3}{4}$

Q.4 What fraction of a day is 8 hours?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Since, a day has 24 hours and we have 8 hours
$?$ Required fraction = $\frac{8}{24}$

Q.5 What fraction of an hour is 40 minutes?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Since 1 hours = 60 minutes
$?$ Fraction of 40 minutes = $\frac{40}{60}$

Q.6 Arya, Abhimanyu, and Vivek shared lunch. Arya has brought two sandwiches, one made of vegetable and one of jam. The other two boys forgot to bring their lunch. Arya agreed to share his sandwiches so that each person will have an equal share of each sandwich.
(a) How can Arya divide his sandwiches so that each person has an equal share?
(b) What part of a sandwich will each boy receive?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) Arya has divided the sandwich into 3 equal parts. So each person will get one part.
(b) Each boy receive $\frac{1}{3}$

Q.7 Kanchan dyes dresses. She had to dye 30 dresses. She has so far finished 20 dresses. What fraction of dresses has she finished?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Total number of dresses to be dyed = 30
Number of dresses finished = 20
$?$ Required fraction = $\frac{20}{30}=\frac{2}{3}$

Q.8 Write the natural numbers from 2 to 12. What fraction of them are prime numbers?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Natural numbers between 2 and 12 are;
2,3,4, 5, 6, 7, 8, 9, 10,11, 12
No. of given natural numbers = 11
No. of prime numbers = 5
Hence, fraction = $\frac{5}{11}$

Q.9 Write the natural numbers from 102 to 113. What fraction of them are prime numbers?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Natural numbers from 102 to 113 are;
102,103,104,105,106, 107,108, 109,110, 111, 112,113
Total number of given natural numbers = 12
Prime numbers are 103, 107, 109, 113 Number of prime numbers = 4
Hence, fraction = $\frac{4}{12}$ = $\frac{1}{3}$

Q.10 What fraction of these circles have X’s in them?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Total number’of circles = 8
Number of circles having X’s in them = 4
Required fraction = $\frac{4}{8}=\frac{1}{2}$

Q.11 Kristin received a CD player for her birthday. She bought 3 CDs and received 5 others as gifts. What fraction of her total CDs did she buy and what fraction did she receive as gifts?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Number of CDs bought by her from the market = 3
Therefore Total number of CDs = 3 + 5 = 8
Therefore Fraction of CDs (bought) = $\frac{3}{8}$
and the fraction of CDs (gifted) = $\frac{5}{8}$

## NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.2

Q.1 Draw number lines and locate the points on them:
(a)$\frac{1}{2},\frac{1}{4},\frac{3}{4},\frac{4}{4}$
(b) $\frac{1}{8},\frac{2}{8},\frac{3}{8},\frac{7}{8}$
(c) $\frac{2}{5},\frac{3}{5},\frac{8}{5},\frac{4}{5}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

Q.2 Express the following as mixed fractions:
(a)$\frac{20}{3}$
(b) $\frac{11}{5}$
(c) $\frac{17}{7}$
(d) $\frac{28}{5}$
(e) $\frac{19}{6}$
(f) $\frac{35}{9}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a)$\frac{20}{3}$ = $6\frac{2}{3}$
(b) $\frac{11}{5}$ = $2\frac{1}{5}$
(c) $\frac{17}{7}$ = $2\frac{3}{7}$
(d) $\frac{28}{5}$ = $5\frac{3}{5}$
(e) $\frac{19}{6}$ = $3\frac{1}{6}$
(f) $\frac{35}{9}$ = $3\frac{8}{9}$

Q.3 Express the following as improper fractions:
(a) $7\frac{3}{4}$
(b) $5\frac{6}{7}$
(c) $2\frac{5}{6}$
(d) $10\frac{3}{5}$
(e) $9\frac{3}{7}$
(f) $8\frac{4}{9}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) $\frac{\left(7×4+3\right)}{4}=\frac{31}{4}$

$?$ The improper form is $\frac{31}{4}$
(b) $\frac{\left(5×7+6\right)}{7}=\frac{41}{7}$

$?$ The improper form is $\frac{41}{7}$
(c) $\frac{\left(2×6+5\right)}{6}=\frac{17}{6}$

$?$ The improper form is $\frac{17}{6}$
(d) $\frac{\left(10×5+3\right)}{5}=\frac{53}{5}$

$?$ The improper form is $\frac{53}{5}$
(e) $\frac{\left(9×7+3\right)}{7}=\frac{66}{7}$

$?$ The improper form is $\frac{66}{7}$
(f) $\frac{\left(8×9+4\right)}{9}=\frac{76}{9}$

$?$ The improper form is $\frac{76}{9}$

## NCERT solutions for class 6 Maths Chapter 7 Fractions Exercise 7.3

Q.1 Write the fractions. Are all these fractions equivalent?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a)
(i) The shaded portion is $\frac{1}{2}$
(ii) The shaded portion is$\frac{2}{4}=\frac{1}{2}$
(iii) The shaded portion is $\frac{3}{6}=\frac{1}{2}$
(iv) The shaded portion is $\frac{4}{8}=\frac{1}{2}$
Hence, all fractions are equivalent.
(b)
(i) The shaded portion is $\frac{4}{12}=\frac{1}{3}$
(ii) The shaded portion is$\frac{3}{9}=\frac{1}{3}$
(iii) The shaded portion is $\frac{2}{6}=\frac{1}{3}$
(iv) The shaded portion is $\frac{6}{15}=\frac{2}{5}$
Hence, all fractions are not equivalent.

Q.2 Write the fractions and pair up the equivalent fractions from each row.

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a)$\frac{1}{2}$
(b) $\frac{4}{6}$ = $\frac{2}{3}$
(c) $\frac{3}{9}$ = $\frac{1}{3}$
(d) $\frac{2}{8}$ = $\frac{1}{4}$
(e) $\frac{3}{4}$
(i) $\frac{6}{18}$ = $\frac{1}{3}$
(ii) $\frac{4}{8}$ = $\frac{1}{2}$
(iii) $\frac{12}{16}$ = $\frac{3}{4}$
(iv) $\frac{8}{12}$ = $\frac{2}{3}$
(v) $\frac{4}{16}$ = $\frac{1}{4}$
The following are the equivalent fractions
(a) and (ii)
(b) and (iv)
(c) and (i)
(d) and (v)
(e) and (iii)

Q.3 Replace $?$in each of the following by the correct number:
(a) $\frac{2}{7}=\frac{8}{?}$
(b) $\frac{5}{8}=\frac{10}{?}$
(c) $\frac{3}{5}=\frac{?}{20}$
(d) $\frac{45}{60}=\frac{15}{?}$
(e) $\frac{18}{24}=\frac{?}{4}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) $\frac{2}{7}=\frac{8}{?}$
$?$ $\frac{2×4}{7×4}=\frac{8}{28}$
(b) $\frac{5}{8}=\frac{10}{?}$
$?$ $\frac{5×2}{8×2}=\frac{10}{16}$
(c) $\frac{3}{5}=\frac{?}{20}$
$?$ $\frac{3×4}{5×4}=\frac{12}{20}$
(d) $\frac{45}{60}=\frac{15}{?}$
$?$ $\frac{45÷3}{60÷3}=\frac{15}{20}$
(e) $\frac{18}{24}=\frac{?}{4}$
$?$ $\frac{18÷6}{24÷6}=\frac{3}{4}$

Q.4 Find the equivalent fraction of $\frac{3}{5}$having
(a) denominator 20
(b) numerator 9
(c) denominator 30
(d) numerator 27

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) We require denominator 20
Let M be the numerator of the fractions
$?\frac{M}{20}={\text{\(}}\frac{3}{5}$
5 × M = 20 × 3
M = (20 × 3) ÷ 5 = 12
Therefore the required fraction is $\frac{12}{20}$
(b) We require numerator 9
Let N be the denominator of the fractions
$?\frac{9}{N}={\text{\(}}\frac{3}{5}$
3 × N = 9 × 5
N = (9 × 5) ÷ 3 = 15
Therefore the required fraction is $\frac{9}{15}$
(c) We require denominator 30
Let D be the numerator of the fraction
$?\frac{D}{30}={\text{\(}}\frac{3}{5}$
5 × D = 3 × 30
D = (3 × 30) ÷ 5
= 18
Therefore the required fraction is $\frac{18}{30}$
(d) We require numerator 27
Let X be the denominator of the fraction
$?\frac{27}{X}={\text{\(}}\frac{3}{5}$
3 × X = 5 × 27
X = (5 × 27) ÷ 3 = 45
Therefore the required fraction is $\frac{27}{45}$

Q.5 Find the equivalent fraction of 36 / 48 with
(a) numerator 9
(b) denominator 4

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) Given numerator = 9
$?\frac{9}{X}=\frac{36}{48}$

X × 36 = 9 × 48
X = (9 × 48) / 36
X = 12
Hence, the equivalent fraction is $\frac{9}{12}$
(b) Given, denominator = 4
$?\frac{X}{4}=\frac{36}{48}$

X × 48 = 4 × 36
X = (4 × 36) / 48 = 3
Hence, the equivalent fraction is $\frac{3}{4}$

Q.6 Check whether the given fractions are equivalent:
(a) $\frac{5}{9},\frac{30}{54}$
(b) $\frac{3}{10},\frac{12}{50}$
(c) $\frac{7}{13},\frac{5}{11}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) Given $\frac{5}{9}$ and $\frac{30}{54}$
We have 5× 54 = 270
9 × 30 = 270
5 × 54 = 9 × 30
Hence, $\frac{5}{9}$ and $\frac{30}{54}$ are equivalent fractions
(b) Given $\frac{3}{10}$ and $\frac{12}{50}$
We have 3 × 50 = 150
10 × 12 = 120
3 × 50 $?$10 × 12
Hence, $\frac{3}{10}$ and $\frac{12}{50}$ are not equivalent fractions
(c) Given $\frac{7}{13}$ and $\frac{5}{11}$

We have 7 × 11 = 77
5 × 13 = 65
7 × 11 $?$ 5 × 13
Hence, $\frac{7}{13}$ and $\frac{5}{11}$ are not equivalent fractions

Q.7 Reduce the following fractions to simplest form:
(a) $\frac{48}{60}$
(b) $\frac{150}{60}$
(c) $\frac{84}{98}$
(d) $\frac{12}{52}$
(e) $\frac{7}{28}$

NCERT Solutions for Class 6 Maths Chapter 7 Fractions

(a) $\frac{48}{60}$ = $\frac{48÷12}{60÷12}$
= $\frac{4}{5}$
(b) $\frac{150}{60}$ = $\frac{150÷30}{60÷30}$
= $\frac{5}{2}$
(c) $\frac{84}{98}$= $\frac{84÷14}{98÷14}$
= $\frac{6}{7}$
(d) $\frac{12}{52}$ = $\frac{12÷4}{52÷4}$
= $\frac{3}{13}$
(e) $\frac{7}{28}$ = $\frac{7÷7}{28÷7}$
= $\frac{1}{4}$

Q.8 Ramesh had 20 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils?

NCERT Solutions for Class 6 Maths Chapter 7 Fractions